Pascal's pyramid

In mathematics, Pascal's pyramid is a three dimensional generalization of Pascal's triangle. Just as Pascal's triangle gives coefficients for the terms of a binomial expansion, so Pascal's pyramid gives coefficients for a trinomial expansion.

Pascal's pyramid is also called Pascal's tetrahedron. A generalization to arbitrary dimension is sometimes called a Pascal's simplex.

The pyramid is constructed layer by layer, starting with the apex and working downward. The first few layers are as follows.

1      1         1              1                   1
     1   1     2   2          3   3               4   4
             1   2   1      3   6   3           6  12   6
                          1   3   3   1       4  12   12  4
                                            1   4   6   4   1

External links

• Beyond Flatland: Geometry for the 21st Century. PART I: Pascal's Tetrahedron

• Pascal's Simplices (discusses Pascal's triangle, Pascal's pyramid, and more)